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Chapter 3: Problem 20

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=6^{x}$$

Short Answer

Expert verified
The graph of the exponential function \(f(x)=6^{x}\) starts near zero when x is negative, passes through the point (0,1), and then rapidly increases for positive x.

Step by step solution

01

Build a Table of Values Using the Graphing Utility

Choose a range of x-values to plug into the function. This range can be from -2 to 2. Using the graphing utility, calculate corresponding y-values. The results might look like this: \n\nx | f(x)\n-2 | 0.02777778 \n-1 | 0.1666667\n 0 | 1\n 1 | 6\n 2 | 36
02

Sketch the graph of the function f(x)

With these points from the table, it is possible to make a rough sketch of the graph. Start by labeling the x- and y-axes from negative 3 to positive 3. Plot the points, then connect them with a smooth curve starting from nearly zero at x = -2 to 36 at x = 2. Remember, the graph of an exponential function has the property of never touching the x-axis, meaning it asymptotically approaches it.

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Most popular questions from this chapter

Determine the time necessary for $$\$ 1000$$to double if it is invested at interest rate \(r\) compounded (a) annually, (b) monthly, (c) daily, and (d) continuously. $$r=6.5 \%$$

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